Harnack inequality for minimizers of integral functionals with general growth conditions (Q1914381)

In this paper the authors prove the Harnack inequality for minimizers of integral functionals of the calculus of variations of the type \[ \int_\Omega f \bigl( |Du |\bigr) dx. \] They assume that \(f\) satisfies some conditions which allow nonstandard growth such as \[ c_1 t^p - c_2 \leq f(t) \leq c_3 t^m + c_4 \] with \(c_i \in R_+\) and \(1 < p < m\).